A mass M hangs from a spring as shown If the mass is pulled down a small distanc

Question

A mass M hangs from a spring as shown If the mass is pulled down a small distance y from its equilibrium position and released, the system will oscillate up and down. If the mass is instead pulled down a distance 2y. will the period of oscillation for the spring-mass system be greater than, less than, or equal to the period of oscillation of the same spring-mass system when it w as pulled down a distance y? Explain. If this spring-mass system were given a larger total energy, would the period of oscillation (the time for one complete cycle of motion) increase, decrease, or remain the same? Explain. If an additional mass is added to the original mass M, will the period of oscillation for the spring-mass system be greater than, less than, or equal to the period of the spring-mass system with only mass M? Explain.

Explanation / Answer

(a)

Period of oscillation,

T = 2*pi *root(L/g) ...(1)

T increases as L increases. So when it's pulled down 2y distance, the period will be bigger compared to when it pullede down y distance.

(b)

Equation (1), doesent have any term related to energy, so it will remain same.

(c)

T = 2*pi*root(m/k)

As m increases, T- period increases. It will increase in this case.

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